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Focal polarization is necessary for finely arranged cell-cell interactions. The yeast mating projection, with its punctate polarisome, is a good model system for this process. We explored the critical role of the polarisome scaffold protein Spa2 during yeast mating with a hypothesis motivated by mathematical modeling and tested by in vivo experiments. Our simulations predicted that two positive feedback loops generate focal polarization, including a novel feedback pathway involving the N-terminal domain of Spa2. We characterized the latter using loss-of-function and gain-of-function mutants. The N-terminal region contains a Spa2 Homology Domain (SHD) which is conserved from yeast to humans, and when mutated largely reproduced the spa2Δ phenotype. Our work together with published data show that the SHD domain recruits Msb3/4 that stimulates Sec4-mediated transport of Bud6 to the polarisome. There, Bud6 activates Bni1-catalyzed actin cable formation, recruiting more Spa2 and completing the positive feedback loop. We demonstrate that disrupting this loop at any point results in morphological defects. Gain-of-function perturbations partially restored focal polarization in a spa2 loss-of-function mutant without restoring localization of upstream components, thus supporting the pathway order. Thus, we have collected data consistent with a novel positive feedback loop that contributes to focal polarization during pheromone-induced polarization in yeast.

We present a new weakly-compressible smoothed particle hydrodynamics (SPH) method capable of modeling non-slip fixed and moving wall boundary conditions. The formulation combines a boundary volume fraction (BVF) wall approach with the transport-velocity SPH method. The resulting method, named SPH-BVF, offers detection of arbitrarily shaped solid walls on-the-fly, with small computational overhead due to its local formulation. This simple framework is capable of solving problems that are difficult or infeasible for standard SPH, namely flows subject to large shear stresses or at moderate Reynolds numbers, and mass transfer in deformable boundaries. In addition, the method extends the transport-velocity formulation to reaction-diffusion transport of mass in Newtonian fluids and linear elastic solids, which is common in biological structures. Taken together, the SPH-BVF method provides a good balance of simplicity and versatility, while avoiding some of the standard obstacles associated with SPH: particle penetration at the boundaries, tension instabilities and anisotropic particle alignments, that hamper SPH from being applied to complex problems such as fluid-structure interaction in a biological system.

Objective: Examine sequence of weakness in arm muscles from longitudinal hand-held dynamometry (HHD) data in ALS for congruence with contiguous spread of neurodegeneration along spinal cord segments. Methods: Longitudinal HHD data from the Ceftriaxone clinical trial were examined using nonlinear mixed models, assuming a logistic trajectory from normal to zero strength. Unobserved baseline normal strength of weak muscles was assumed using strength of the best-preserved muscle. A novel metric called “time from onset to midway strength” (TOMS) was estimated for each muscle group, and TOMS ratios were examined to identify sequence of weakness, overall and by onset site. Results: Shoulder flexion (SF), elbow flexion (EF), elbow extension (EE), wrist extension (WE), and first dorsal interosseous (FDI) were measured on each side. Over a median of 36 weeks, 513 subjects provided 2589 sets of HHD measures. TOMS increased sequentially in the following order: FDI, WE, SF, EF, and EE. TOMS ratios estimates with 95% CIs (adjusted for multiple comparisons) were: WE/FDI 1.32 (1.24–1.41), SF/WE 1.06 (1.01–1.10), EF/SF 1.06 (1.02–1.10), and EE/EF 1.18 (1.12–1.23). Elbow and shoulder flexors weakened sooner than did elbow extensors. The sequence of arm muscle weakness progression was similar regardless of onset site. Conclusion: Nonsegmental progression of arm muscle weakness that is similar for different onset sites favors cortical influence/network spread over contiguous spread of neurodegeneration in the spinal cord. Furthermore, this study confirms the “split elbow” pattern. TOMS and other proposed methods may have value as outcome measures in clinical research.

Many cellular processes require cell polarization to be maintained as the cell changes shape, grows or moves. Without feedback mechanisms relaying information about cell shape to the polarity molecular machinery, the coordination between cell polarization and morphogenesis, movement or growth would not be possible. Here we theoretically and computationally study the role of a genetically-encoded mechanical feedback (in the Cell Wall Integrity pathway) as a potential coordination mechanism between cell morphogenesis and polarity during budding yeast mating projection growth. We developed a coarse-grained continuum description of the coupled dynamics of cell polarization and morphogenesis as well as 3D stochastic simulations of the molecular polarization machinery in the evolving cell shape. Both theoretical approaches show that in the absence of mechanical feedback (or in the presence of weak feedback), cell polarity cannot be maintained at the projection tip during growth, with the polarization cap wandering off the projection tip, arresting morphogenesis. In contrast, for mechanical feedback strengths above a threshold, cells can robustly maintain cell polarization at the tip and simultaneously sustain mating projection growth. These results indicate that the mechanical feedback encoded in the Cell Wall Integrity pathway can provide important positional information to the molecular machinery in the cell, thereby enabling the coordination of cell polarization and morphogenesis., Author summary Cell migration, morphogenesis and secretion are among the vast number of cellular processes that require cells to define a preferred spatial direction to perform essential tasks. This is achieved by setting an intracellular molecular gradient that polarizes the cell. While the molecular players involved in cell polarization and some of the mechanisms that cells use to establish such molecular gradients are known, it remains unclear how cells maintain polarization as they dramatically change shape during morphogenesis, migration, etc. Here we identify a potential feedback control mechanism, encoded genetically in cells, that provides the molecular polarization machinery with the necessary information about cell geometry to maintain cell polarization during cell shape changes.

Many cellular processes require cell polarization to be maintained as the cell changes shape, grows or moves. Without feedback mechanisms relaying information about cell shape to the polarity molecular machinery, the coordination between cell polarization and morphogenesis, movement or growth would not be possible. Here we theoretically and computationally study the role of a genetically-encoded mechanical feedback (in the Cell Wall Integrity Pathway) as a potential coordination mechanism between cell morphogenesis and polarity during budding yeast mating projection growth. We developed a coarse-grained continuum description of the coupled dynamics of cell polarization and morphogenesis as well as 3D stochastic simulations of the molecular polarization machinery in the evolving cell shape. Both theoretical approaches show that in the absence of mechanical feedback (or in the presence of weak feedback), cell polarity cannot be maintained at the projection tip during growth, with the polarization cap wandering off the projection tip, arresting morphogenesis. In contrast, for mechanical feedback strengths above a threshold, cells can robustly maintain cell polarization at the tip and simultaneously sustain mating projection growth. These results indicate that the mechanical feedback encoded in the Cell Wall Integrity pathway can provide important positional information to the molecular machinery in the cell, thereby enabling the coordination of cell polarization and morphogenesis.Author summaryCell migration, morphogenesis and secretion are among the vast number of cellular processes that require cells to define a preferred spatial direction to perform essential tasks. This is achieved by setting an intracellular molecular gradient that polarizes the cell. While the molecular players involved in cell polarization and some of the mechanisms that cells use to establish such molecular gradients are known, it remains unclear how cells maintain polarization as they dramatically change shape during morphogenesis, migration, etc. Here we identify a potential feedback control mechanism, encoded genetically in cells, that provides the molecular polarization machinery with the necessary information about cell geometry to maintain cell polarization during cell shape changes.

The localization (or polarization) of proteins on the membrane during the mating of budding yeast (Saccharomyces cerevisiae) is an important model system for understanding simple pattern formation within cells. While there are many existing mathematical models of polarization, for both budding and mating, there are still many aspects of this process that are not well understood. In this paper we set out to elucidate the effect that the geometry of the cell can have on the dynamics of certain models of polarization. Specifically, we look at several spatial stochastic models of Cdc42 polarization that have been adapted from published models, on a variety of tip-shaped geometries, to replicate the shape change that occurs during the growth of the mating projection. We show here that there is a complex interplay between the dynamics of polarization and the shape of the cell. Our results show that while models of polarization can generate a stable polarization cap, its localization at the tip of mating projections is unstable, with the polarization cap drifting away from the tip of the projection in a geometry dependent manner. We also compare predictions from our computational results to experiments that observe cells with projections of varying lengths, and track the stability of the polarization cap. Lastly, we examine one model of actin polarization and show that it is unlikely, at least for the models studied here, that actin dynamics and vesicle traffic are able to overcome this effect of geometry., Author summary The ability of cells to spontaneously break symmetry and form patterns via networks of protein reactions is a well-studied, yet not fully understood, phenomenon. One particularly useful model system is the mating of yeast cells, where a localization of proteins on the membrane leads to actin cable formation, vesicle traffic, changes in material properties of the cell wall and ultimately to the growth of a mating projection. There is no shortage of mathematical models describing the mechanisms of polarization, yet they are often formulated as differential equations on simple domains. The effect of geometry on the dynamics of polarization has not been systematically explored. There is an interaction between the length scales of polarization and the features of the geometry of the cell that has been under-appreciated and may lead to novel biological insights.

Recent outbreaks of chytridiomycosis, the disease of amphibians caused by the fungal pathogen Batrachochytrium dendrobatidis (Bd), have contributed to population declines of numerous amphibian species worldwide. The devastating impacts of this disease have led researchers to attempt drastic conservation measures to prevent further extinctions and loss of biodiversity. The conservation measures can be labour-intensive or expensive, and in many cases have been unsuccessful. We developed a mathematical model of Bd outbreaks that includes the effects of demographic stochasticity and within-host fungal load dynamics. We investigated the impacts of one-time treatment conservation strategies during the disease outbreak that occurs following the initial arrival of Bd into a previously uninfected frog population. We found that for all versions of the model, for a large fraction of parameter space, none of the one-time treatment strategies are effective at preventing disease-induced extinction of the amphibian population. Of the strategies considered, treating frogs with antifungal agents to reduce their fungal load had the greatest likelihood of a beneficial outcome and the lowest risk of decreasing the persistence of the frog population, suggesting that this disease mitigation strategy should be prioritized over disinfecting the environment or reducing host density.

© 2016 Drawert et al. We present StochSS: Stochastic Simulation as a Service, an integrated development environment for modeling and simulation of both deterministic and discrete stochastic biochemical systems in up to three dimensions. An easy to use graphical user interface enables researchers to quickly develop and simulate a biological model on a desktop or laptop, which can then be expanded to incorporate increasing levels of complexity. StochSS features state-of-the-art simulation engines. As the demand for computational power increases, StochSS can seamlessly scale computing resources in the cloud. In addition, StochSS can be deployed as a multi-user software environment where collaborators share computational resources and exchange models via a public model repository. We demonstrate the capabilities and ease of use of StochSS with an example of model development and simulation at increasing levels of complexity.

GillesPy is an open-source Python package for model construction and simulation of stochastic biochemical systems. GillesPy consists of a Python framework for model building and an interface to the StochKit2 suite of efficient simulation algorithms based on the Gillespie stochastic simulation algorithms (SSA). To enable intuitive model construction and seamless integration into the scientific Python stack, we present an easy to understand, action-oriented programming interface. Here, we describe the components of this package and provide a detailed example relevant to the computational biology community.

In this paper, we present the design and implementation of Neptune, a simple, domain-specific language based on the Ruby programming language. Neptune automates the configuration and deployment of scientific software frameworks over disparate cloud computing systems. Neptune integrates support for MPI, MapReduce, UPC, X10, StochKit, and others. We implement Neptune as a software overlay for the AppScale cloud platform and extend AppScale with support for elasticity and hybrid execution for scientific computing applications. Neptune imposes no overhead on application execution, yet significantly simplifies the application deployment process, enables portability across cloud systems, and promotes lock-in avoidance by specific cloud vendors.

Computational experiments using spatial stochastic simulations have led to important new biological insights, but they require specialized tools and a complex software stack, as well as large and scalable compute and data analysis resources due to the large computational cost associated with Monte Carlo computational workflows. The complexity of setting up and managing a large-scale distributed computation environment to support productive and reproducible modeling can be prohibitive for practitioners in systems biology. This results in a barrier to the adoption of spatial stochastic simulation tools, effectively limiting the type of biological questions addressed by quantitative modeling. In this paper, we present PyURDME, a new, user-friendly spatial modeling and simulation package, and MOLNs, a cloud computing appliance for distributed simulation of stochastic reaction-diffusion models. MOLNs is based on IPython and provides an interactive programming platform for development of sharable and reproducible distributed parallel computational experiments.

In this paper, we present CLOUDRUNNER, a framework that extracts arbitrary programs from a source code repository (e.g. GitHub), wraps them in a web service and tasking system, and deploys them over disparate cloud infrastructures and local clusters, automating their portability. In particular, CLOUDRUNNER automatically creates and configures virtual machines so that they can execute the applications, provides a web UI with which users parameterize their applications, deploys instances of the program as background tasks, and collects the results for easy access via a browser. CLOUDRUNNER is an ideal framework for deploying scientific simulation applications portably and as such, we use it to implement StochSS - Stochastic Simulation as-a-service (now available at http://www.stochss.org). We use StochSS to evaluate CLOUDRUNNER overheads and find that they are small, consistent, and amortized for even short running applications.

The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent properties of exact kinetic-Monte Carlo simulation methods limit the efficiency of parallel implementations. Several approximate and hybrid methods have appeared that enable more efficient simulation of the RDME. A common feature to most of them is that they rely on splitting the system into its reaction and diffusion parts and updating them sequentially over a discrete timestep. This use of operator splitting enables more efficient simulation but it comes at the price of a temporal discretization error that depends on the size of the timestep. So far, existing methods have not attempted to estimate or control this error in a systematic manner. This makes the solvers hard to use for practitioners since they must guess an appropriate timestep. It also makes the solvers potentially less efficient than if the timesteps were adapted to control the error. Here, we derive estimates of the local error and propose a strategy to adaptively select the timestep when the RDME is simulated via a first order operator splitting. While the strategy is general and applicable to a wide range of approximate and hybrid methods, we exemplify it here by extending a previously published approximate method, the diffusive finite-state projection (DFSP) method, to incorporate temporal adaptivity.

In this work, we investigate tools that enable dollar cost optimization of scientific simulations using commercial clouds. We present a framework, called CloudTracker, that transparently records information from a simulation that is executed in a commercial cloud so that it may be “replayed” exactly to reproduce its results. Using the automated CloudTracker provenance and replay facilities, scientists can choose either to store the results of a simulation or to reproduce it on-demand – whichever is more cost efficient in terms of the dollar cost charged for storage and computing by the commercial cloud provider. We present a prototype implementation of CloudTracker for the Amazon AWS commercial cloud and the StochSS stochastic simulation system. Using this prototype, we analyze the storage-versus-compute cost tradeoffs for different classes of StochSS simulations when deployed and executed in AWS.

Although cell polarity is an essential feature of living cells, it is far from being well-understood. Using a combination of computational modeling and biological experiments we closely examine an important prototype of cell polarity: the pheromone-induced formation of the yeast polarisome. Focusing on the role of noise and spatial heterogeneity, we develop and investigate two mechanistic spatial models of polarisome formation, one deterministic and the other stochastic, and compare the contrasting predictions of these two models against experimental phenotypes of wild-type and mutant cells. We find that the stochastic model can more robustly reproduce two fundamental characteristics observed in wild-type cells: a highly polarized phenotype via a mechanism that we refer to as spatial stochastic amplification, and the ability of the polarisome to track a moving pheromone input. Moreover, we find that only the stochastic model can simultaneously reproduce these characteristics of the wild-type phenotype and the multi-polarisome phenotype of a deletion mutant of the scaffolding protein Spa2. Significantly, our analysis also demonstrates that higher levels of stochastic noise results in increased robustness of polarization to parameter variation. Furthermore, our work suggests a novel role for a polarisome protein in the stabilization of actin cables. These findings elucidate the intricate role of spatial stochastic effects in cell polarity, giving support to a cellular model where noise and spatial heterogeneity combine to achieve robust biological function., PLoS Computational Biology, 9 (7), ISSN:1553-734X, ISSN:1553-7358

We have developed a method for modeling spatial stochastic biochemical reactions in complex, three-dimensional, and time-dependent domains using the reaction-diffusion master equation formalism. In particular, we look to address the fully coupled problems that arise in systems biology where the shape and mechanical properties of a cell are determined by the state of the biochemistry and vice versa. To validate our method and characterize the error involved, we compare our results for a carefully constructed test problem to those of a microscale implementation. We demonstrate the effectiveness of our method by simulating a model of polarization and shmoo formation during the mating of yeast. The method is generally applicable to problems in systems biology where biochemistry and mechanics are coupled, and spatial stochastic effects are critical.

Background Experiments in silico using stochastic reaction-diffusion models have emerged as an important tool in molecular systems biology. Designing computational software for such applications poses several challenges. Firstly, realistic lattice-based modeling for biological applications requires a consistent way of handling complex geometries, including curved inner- and outer boundaries. Secondly, spatiotemporal stochastic simulations are computationally expensive due to the fast time scales of individual reaction- and diffusion events when compared to the biological phenomena of actual interest. We therefore argue that simulation software needs to be both computationally efficient, employing sophisticated algorithms, yet in the same time flexible in order to meet present and future needs of increasingly complex biological modeling. Results We have developed URDME, a flexible software framework for general stochastic reaction-transport modeling and simulation. URDME uses U nstructured triangular and tetrahedral meshes to resolve general geometries, and relies on the R eaction-D iffusion M aster E quation formalism to model the processes under study. An interface to a mature geometry and mesh handling external software (Comsol Multiphysics) provides for a stable and interactive environment for model construction. The core simulation routines are logically separated from the model building interface and written in a low-level language for computational efficiency. The connection to the geometry handling software is realized via a Matlab interface which facilitates script computing, data management, and post-processing. For practitioners, the software therefore behaves much as an interactive Matlab toolbox. At the same time, it is possible to modify and extend URDME with newly developed simulation routines. Since the overall design effectively hides the complexity of managing the geometry and meshes, this means that newly developed methods may be tested in a realistic setting already at an early stage of development. Conclusions In this paper we demonstrate, in a series of examples with high relevance to the molecular systems biology community, that the proposed software framework is a useful tool for both practitioners and developers of spatial stochastic simulation algorithms. Through the combined efforts of algorithm development and improved modeling accuracy, increasingly complex biological models become feasible to study through computational methods. URDME is freely available at http://www.urdme.org.

We have developed a computational framework for accurate and efficient simulation of stochastic spatially inhomogeneous biochemical systems. The new computational method employs a fractional step hybrid strategy. A novel formulation of the finite state projection (FSP) method, called the diffusive FSP method, is introduced for the efficient and accurate simulation of diffusive transport. Reactions are handled by the stochastic simulation algorithm.